Inter-comparison of remotely-sensed actual evapotranspiration products in the Zayandehrud river basin, Iran

<p>Accurate estimation of evapotranspiration (ET) helps to create a better understanding of water allocation, irrigation scheduling, and crop management especially in arid and semiarid regions where agricultural areas are far more affected by water shortage and drought events. Remote sensing (RS) facilitates estimating the ET in regions where long-term field measurements are missed.  In this study, we compare the performance of free open-access remotely sensed actual ET products at eleven counties of the Zayandehrud basin. The Zayandehrud basin, one of the major watersheds of Iran, suffers from recurrent droughts and long-term impacts of aridity. The RS products used in this study are namely WaPOR (2009-2019), MOD16A2 (2003-2019), SSEBOp (2003-2019). We also merged the two products of SSEBOp and WaPOR and assessed its performance. To prepare the Merged ETa Product (MEP), WaPOR was resampled to the spatial resolution of SSEBOp. Then, the average pixel values of the resampled ETa product and SSEBOp were calculated. To compare ETa estimations over croplands in each county, maximum Normalized Difference Vegetation Index (NDVI) maps at annual scale (2003-2019) were prepared using LANDSAT 5, 7, and 8 images. Annual mean ETa estimations were then extracted over croplands by using annual maximum NDVI layers. We compared the RS-based ETa with reported long-term ETa values extracted from the local available literature. Our results showed a consistent underestimation of MOD16A2 in all counties. The MEP and WaPOR outperformed other products in the estimation of ETa in seven. Estimations of WaPOR and SSEBOp agreed in most of the counties. Our analysis displayed that, although MOD16A2 underestimated ETa values, it could together with SSEBOp capture the drought better than that of WaPOR and MEP in the lower reaches of the basin. Further study is needed to evaluate the monthly and seasonal performance of RS-based ETa products.</p>

CONGRUENCES MODULO 4 FOR WEIGHT ETA-PRODUCTS

We find and prove a class of congruences modulo 4 for eta-products associated with certain ternary quadratic forms. This study was inspired by similar conjectured congruences modulo 4 for certain mock theta functions.

Evaluation of precipitation and actual evaporation products over the Nile Basin

<p>An improved representation of the spatio-temporal patterns of climatological variables is crucial for ecological, agricultural, and hydrological applications and can improve the decision-making process. Traditionally, precipitation (P) and actual evaporation (ETa) are estimated using ground-based measurements from meteorological stations. However, the estimation of spatial patterns derived solely from point-based measurements is subject to large uncertainties, particularly in data-scarce regions as the Nile Basin, which has an area of about 3 million km<sup>2</sup>. This study evaluates six state-of-the-art P products (CHIRPSv2, CMORPHv1, CRU TS4.02, MSWEPv2.2, PERSIANN-CDR and GPCCv2018) and five ETa products (SSEBop, MOD16-ET, WaPOR, GLEAM and GLDAS) over the Nile Basin to identify the best-performing products. The P products were evaluated at monthly and annual temporal scales (from 1983 onwards) through a point-to-pixel approach using the modified Kling-Gupta Efficiency and its components (linear correlation, bias, and variability ratio) as continuous performance indices. The ETa products were evaluated through the water balance approach (due to the lack of ground-based ETa measurements) for 2009-2018 at the multiannual scale. Because streamflow data were not available for this period, an empirical model based on the Random Forest machine learning technique was used to estimate streamflow at 21 catchments at the monthly scale. For this purpose, we used streamflow data from 1983 to 2005 as the dependent variable, while CHIRPSv2 precipitation and ERA5 potential evaporation and temperature data were used as predictors. For the catchments where the model performed well over the validation period, streamflow estimates were generated and used for the water balance analysis. Our results show that CHIRPSv2 was the best performing P product at monthly and annual scale when compared with ground-based measurements, while WaPOR was the best-performing ETa product in the water balance evaluation. This study demonstrates how remote sensing data can be evaluated over extremely data-scarce scenarios to estimate the magnitude of key meteorological variables, yet also highlights the importance of improving data availability so that the characterisation of these variables can be further evaluated and improved.</p>

The Performance of Satellite-Based Actual Evapotranspiration Products and the Assessment of Irrigation Efficiency in Egypt

Monitoring of crop water consumption, also known as actual evapotranspiration (ETa), is crucial for the prudent use of limited freshwater resources. Remote-sensing-based algorithms have become a popular approach for providing spatio-temporal information on ETa. Satellite-based ETa products are widely available. However, identifying an adequate product remains a challenge due to validation data scarcity. This study developed an assessment process to identify superior ETa products in agricultural areas in Egypt. The land cover product (MCD12Q1) from Moderate Resolution Imaging Spectroradiometer (MODIS) was evaluated and used to detect agricultural areas. The performances of three ETa products, namely: Earth Engine Evapotranspiration Flux (EEFlux), USGS-FEWS NET SSEBop ETa monthly product, and MODIS ETa monthly product (MOD16A2), were evaluated. The ETa values of these products were compared to previous ETa observations and evaluated using the integrated Normalized Difference Vegetation Index (iNDVI) on a seasonal and annual basis. Finally, the irrigation efficiency throughout Egypt was calculated based on the annual Relative Water Supply (RWS) index. Results reveal that the SSEBop monthly product has the best performance in Egypt, followed by the MOD16A2. The EEFlux overestimated ETa values by 36%. RWS had a range of 0.96–1.47, indicating high irrigation efficiency. The findings reported herein can assist in improving irrigation water management in Egypt and the Nile Basin.

ON REPRESENTATION OF MODULAR FORMS AS HOMOGENEOUS POLYNOMIALS

In the article we study the spaces of modular forms such that each element of them is a homogeneous polynomial of modular forms of low weights of the same level. It is a classical fact that it is true for the level 1. N. Koblitz point out that it is true for cusp forms of level 4. In this article we show that the analogous situation takes place for the levels corresponding to the eta-products with multiplicative coefficients. In all cases under consideration the base functions are eta-products. In each case the base functions are written explicitly. Dimensions of spaces are calculated by the Cohen - Oesterle formula, the orders in cusps are calculated by the Biagioli formula.

Evaluation of different evapotranspiration products in the middle Yellow River Basin, China

Actual evapotranspiration (ETa) is a central process in the climate system and a nexus of the water and energy cycles. This study assesses the hydrological performance of the four categories of ETa products (i.e., land surface models (LSMs), reanalysis, model tree ensemble, and diagnostic models (DMs)) for use in the middle Yellow River Basin (MYRB) using water balance methods. The results show the following. (1) The water storage changes significantly at annual scale and cannot be neglected when calculating the reference ETa by the water balance methods. (2) ETa from LSMs, considering the precipitation input, exhibits the best performance in capturing the reference ETa variation. The MET ETa (AETJUNG), based on eddy covariance, has fair performance with a small underestimation, followed by the DMs, including MODIS and ZhangKe. Poor performance is found in reanalysis ETa (JRA55), due to overestimations precipitation and radiation. (3) The reference ETa showed decreased and then increased trend. ETa from the LSMs-Noah model captures the trend well, followed by the LSMs-variable infiltration capacity model. Our results are not only meaningful for better understanding ETa variability in the MYRB, but also significant for improving global ETa products models' performance in semi-arid and semi-humid regions.